Many non-western musics involve non-isochronous (NI) meters (also known as complex or additive meters), based on cycles of a prime number of rapid articulations (e.g., 7, 11) or uneven divisions of non-prime cycles (e.g., 9 divided 2+2+2+3). As a result, in NI meters one has uneven beats (i.e., more than one class or category of beat intervals). An additional well-formedness constraint, maximal evenness, is given to limit this unevenness; maximal evenness also gives rise to optimal entrainment behaviors. The prevalence for most NI meters to use beats in a 2:3 durational ratio is explained in terms of more general constraints on beat formation (i.e., the speed limits for beat subdivisions and for beats to have similar temporal magnitude). As one may permute or rotate a series of uneven beats, there is an additional “ordering constraint” on NI-metrical types. Accent in the context of NI meters is also considered.
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